Graph Theory with Applications to Engineering and Computer Science

This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra. Topics include paths and circuits, trees and fundamental circuits, planar and dual graphs, vector and matrix representation of graphs, and related subjects.
The remaining six chapters are more advanced, covering graph theory algorithms and computer programs, graphs in switching and coding theory, electrical network analysis by graph theory, graph theory in operations research, and more. Instructors may combine these chapters with the preceding material for courses in a variety of fields, including electrical engineering, computer science, operations research, and applied mathematics.

Table of Contents

Chapter 1 Introduction
Chapter 2 Paths And Circuits
Chapter 3 Trees And Fundamental Circuits
Chapter 4 Cut-Sets And Cut-Vertices
Chapter 5 Planar And Dual Graphs
Chapter 6 Vector Spaces Of A Graph
Chapter 7 Matrix Representation Of Graphs
Chapter 8 Coloring, Covering, And Partitioning
Chapter 9 Directed Graphs
Chapter 10 Enumeration Of Graphs
Chapter 11 Graph Theoretic Algorithms And Computer Programs
Chapter 12 Graphs In Switching And Coding Theory
Chapter 13 Electrical Network Analysis By Graph Theory
Chapter 14 Graph Theory In Operations Research
Chapter 15 Survey Of Other Applications
Appendix A Binet-Cauchy Theorem
Appendix B Nullity Of A Matrix And Sylvester’S Law